# Algebra HELP – Word Problem#1 – Roller Coaster Crew

Roller Coaster Crew

Ray and Kelsey accept summer internships at an engineering resolute. As bisect of their internship, they get to relieve in the contemplationning of a mark new roller coaster. For this assignment, you aid Ray and Kelsey as they gear the math following some ultimate flexions in the coaster's trace.

Part A

The original bisect of Ray and Kelsey's roller coaster is a deflexed sample that can be represented by a polynomial duty.

1. Ray and Kelsey are established to graph a third-degree polynomial duty that represents the original sample in the coaster contemplation. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the duty can accept as sundry as 3 zeros merely. Is there a way for the twain of them to be rectify? Explain your tally.
2. Kelsey has a schedule of potential dutys. Pick one of the g(x) dutys underneath and then represent to Kelsey the key features of g(x), including the end manner, y-intercept, and zeros.
• g(x) = x3 − x2 − 4x + 4
• g(x) = x3 + 2x2 − 9x − 18
• g(x) = x3 − 3x2 − 4x + 12
• g(x) = x3 + 2x2 − 25x − 50
• g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial duty you clarified from Question 2.

Part B

The relieve bisect of the new coaster is a parabola.

1. Ray needs aid creating the relieve bisect of the coaster. Create a uncommon parabola in the sample f(x) = ax2 + bx + c. Represent the control of the parabola and state the y-intercept and zeros.
2. The prophylactic supervisor notes that Ray besides needs to contemplation for a perpendicular ladder through the nature of the coaster's parabolic fashion for avenue to the coaster to accomplish prophylactic repairs. Find the vertex and the equation for the axis of agreement of the parabola, showing your operation, so Ray can involve it in his coaster contemplation.
3. Create a graph of the polynomial duty you created in Question 4.

Part C

1. Now that the flexion pieces are stated, use those pieces as exceptions of a entire coaster. By laborer or by using a delineation program, paint a guile of Ray and Kelsey's coaster that involves the fashion of the g(x) and f(x) dutys that you chose in the Parts A and B. You do not accept to involve the coordinate contemplatione. You may ordain the dutys in any ordain you prefer, but mark each exception of the graph after a while the corresponding duty for your schoolmistress to light.

Part D

1. Create an ad hostilities to excite Ray and Kelsey's roller coaster. It can be a 15-relieve plan for television or radio, an interlight for a case or information announce, or a carol, carol, or slideshow offer for a gang. These are sound examples; you are not scant to how you equip your plan, so be notional. Make assured to involve a script of what each of you succeed say if you are preparing an interlight or a announce. The scope of this ad is to get everyone distracted about the roller coaster.